\newproblem{lay:4_5_26}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.5.26}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Let $H$ be an $n$-dimensional subspace of an $n$-dimensional vector space $V$. Show that $H=V$.
}{
  % Solution
	Let $B_H$ be a basis of $H$. Since $H$ is an $n$-dimensional vector space, $B_H$ must have $n$ vectors. But by Theorem 9.4 of Chapter 5, any set 
	of $n$ linearly independent vectors of $V$ is a basis of $V$. So $B_H$ is also a basis for $V$. Since both spaces have the same basis, both spaces are the same.
}
\useproblem{lay:4_5_26}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
